Modeling queues at signalized intersections

Traffic control is one of the most effective techniques for a road manager to adapt network capacity to flow. It also provides possibilities to modify users' choices of modes and routes. An important area of research is formed by the dynamic assignment problem, in which the effect of delays at controlled intersections is taken into account. This problem requires realistic queuing models. If the degree of saturation of an intersection is close to or larger than 1.0, the queue size has a dynamic character. The case in which the initial queue is nonzero is similar. Existing queue models have important limitations. A Markov model was developed to calculate the dynamics of the queue. It appears that the variance of the queue length is an important determinant of queue dynamics. The case of decreasing queues is analyzed and shows that available models in this case underestimate the mean values and are barely applicable in modeling time-of-day dynamics. An approximate expression for the case of decreasing queues is provided and analyzed with its parameters. Finally the same approach also suggests an approximate formulation for the evolution of the standard deviation with time and provides better knowledge of the uncertainties at signalized intersections. The analytical model introduced is suited for application in dynamic assignment problems.